Final answer:
The most important center of learning during the Hellenistic Period was the Library of Alexandria, part of the Museon, which was a leading hub for scholarship and housed numerous scrolls and academic advancements.
Step-by-step explanation:
The most important center of learning during the Hellenistic Period was A) the Library of Alexandria. This institution was part of the wider Museon, or Museum of Alexandria, which has often been called the world's first research university. It was a major hub for scholars and intellectuals and held an extraordinary collection of approximately 700,000 scrolls. It also included laboratories and lecture halls, making it the preeminent site of learning in the Hellenistic world. The Library of Alexandria played a crucial role in many academic advancements, including those in the study of geography by Eratosthenes, who estimated the circumference of the Earth.
Other centers of learning, such as Athens Academy and the Pergamon School, were significant but did not match the scale and influence of the Library of Alexandria during this time. Additionally, there is no historical evidence of a 'Cyrene University' holding such distinction in the Hellenistic period.